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Generalized geometric speed limits for quantum observables

Leveraging quantum information geometry, we derive generalized quantum speed limits on the rate of change of the expectation values of observables. These bounds subsume and, for Hilbert space dimension ≥3, tighten existing bounds—in some cases by an arbitrarily large multiplicative constant. Our theoretical results are supported by illustrative examples and an experimental demonstration using a superconducting qutrit. We also derive two upper bounds on the generalized quantum Fisher information in terms of the condition number of the density matrix. One of these bounds applies only to coherent dynamics and depends also on the variance of the Hamiltonian. The other bound depends also on the so-called Wigner-Yanase skew information. These bounds generalize well-known bounds on the symmetric logarithmic derivative quantum Fisher information and are tighter than the existing bounds for sufficiently mixed states (e.g., for sufficiently high temperature thermal states).

open quantum systems & decoherence

Final Technical Report for DE-SC0022206

This project developed foundational genetic, genomic, and epigenetic tools for anaerobic fungi (Neocallimastigomycota), a group of microorganisms with exceptional natural abilities to deconstruct lignocellulosic biomass. Efficient biomass deconstruction remains a major barrier to economical production of renewable fuels, chemicals, and materials from agricultural and forestry residues. The project sought to enable mechanistic studies and future engineering of anaerobic fungi by improving genomic resources, establishing methods for gene expression, and investigating epigenetic regulation of biomass-degrading pathways. Major accomplishments included generation of the first chromosome-scale genome assemblies for multiple anaerobic fungal species, providing publicly available genomic resources that support both engineering and fundamental biological research. The project established the first reproducible system for heterologous gene expression in anaerobic fungi and identified genomic features and mobile genetic elements that may support future development of stable transformation technologies. In parallel, the project demonstrated direct conversion of untreated lignocellulosic biomass into fuels and specialty chemicals through a fungal-yeast bioprocess and identified anaerobic fungal enzymes with utility for metabolic engineering. The research also revealed that epigenetic regulation plays an important role in controlling fungal gene expression and enzyme production, identifying potential strategies for enhancing biomass degradation. Collectively, this work established anaerobic fungi as a tractable emerging platform for bioenergy and biomanufacturing research, generated valuable public resources, trained the next generation of researchers, and advanced DOE-BER goals related to predictive biology, sustainable bioprocessing, and the circular bioeconomy.

Solomon, Kevin [University of Delaware] (ORCID:000

Engineering 2D Square Lattice Hubbard Models in 90° Twisted GeX/SnX (X =S, Se) Moiré Superlattices

Because of the large-period superlattices emerging in moiré two-dimensional (2D) materials, electronic states in such systems exhibit low energy flat bands that can be used to simulate strongly correlated physics in a highly tunable setup. While many investigations have thus far focused on moiré flat bands and emergent correlated electron physics in triangular, honeycomb, and quasi-one-dimensional lattices, tunable moiré realizations of square lattices subject to strong correlations remain elusive. Here, in this work, we propose a feasible scheme to construct moiré square lattice systems by twisting two or more layers of 2D materials in a rectangular lattice by 90°. We demonstrate the concept with twisted GeX/SnX (X =S, Se) moiré superlattices and calculate their electronic structures from first principles. We show that the lowest conduction flat band in these systems can be described by a square lattice Hubbard model with parameters which can be controlled by varying the choice of host materials, number of layers, and external electric fields. In particular, twisted double bilayer GeSe realizes a square lattice Hubbard model with strong frustration due to the next-nearest-neighbor hopping that could host unconventional superconductivity, in close analogy to the Hubbard model for copper-oxygen planes of cuprate high-temperature superconductors. The presented scheme uses 90° twisted 2D materials with rectangular unit cells as a promising platform for realizing the physical phenomena of square lattice Hubbard models, establishing a new route for studying its rich phase diagram of magnetism, charge order, and unconventional superconductivity in a highly tunable setting.

2-dimensional systems

Chronology of ungrouped achondrites Northwest Africa 11119 and 7325/8486: implications for early evolution of a heterogeneous crust on a differentiated planetesimal

The chronology of ungrouped achondrites provides key insights into the timeline of igneous activity in the early Solar System. Two ungrouped achondrites – Northwest Africa (NWA) 11119 (andesite-dacite) and NWA 8486 and its pair NWA 7325 (olivine gabbro) – are the focus of this study, where their chronologies are investigated using multiple high-resolution techniques. Here we report the lead-lead (207Pb-206Pb) and manganese-chromium (53Mn-53Cr) systematics of NWA 11119, as well as the 207Pb-206Pb systematics of NWA 8486 alongside aluminum-magnesium (26Al-26Mg) systematics for NWA 7325. The U-corrected 207Pb-206Pb ages of NWA 11119 and the combined ages of NWA 7325/8486 are 4566.4 ± 0.8 Ma and 4563.8 ± 1.9 Ma, respectively. Additionally, we report the 53Mn-53Cr age of NWA 11119 to be 4564.4 ± 2.5 Ma and the 26Al-26Mg age of NWA 7325/8486 to be 4563.1 ± 0.3 Ma. The formation of NWA 11119 requires partial melting of a (likely chondritic) source reservoir leading to eruption of Si rich, alkali depleted magmas, while NWA 7325/8486 likely formed from a chemically fractionated reservoir with superchondritic Al/Mg. The clear geochemical and isotopic similarities of these achondrites, combined with the chronology reported here, is suggestive of formation of these two ungrouped achondrites on a common parent body which likely formed in the inner Solar System and experienced early differentiation under reducing conditions. If these achondrites did share a parent body, it would suggest that primary asteroids in the early Solar System commonly produced mineralogically and geochemically heterogeneous crusts. While mineralogical and geochemical heterogeneity is known to exist in the (mostly mafic) crust of asteroid Vesta, our findings show that even more significant crustal heterogeneity (representing felsic and mafic compositions) may exist on other asteroids.

Cartwright, Julia [University of Leicester, UK]

Multi-Ion Complexes and Competition from Bulky BArF – Anions for Chloride Binding in Ion Pairing Conditions

Cationic charges have long been used to enhance anion binding. Embedding charge introduces strong ion pairing for target anions but also for off-target ions, ultimately generating a mixture of multi-ion species that are hard to identify and quantify. While many sidestep this problem using polar solvents and weakly coordinating ions, these approaches exclude a substantial cross-section of conditions found in applications spanning recognition, assembly, separations, templation, and catalysis. To confront this complexity, we study the binding of an anion to a cationic receptor featuring low shape complementarity in a low-polarity solvent to maximize ionic interactions. We prepared the receptor as a salt of the weakly coordinating tetrakis­[3,5-bis­(trifluoromethyl)­phenyl]­borate (BArF – ) anion and studied the binding of small chloride (Cl – ) and medium-sized iodide (I – ) anions. Surprisingly, the use of the bulky BArF – anion does not suppress ion pairing interactions, with 65% of the receptor being paired at 0.5 mM in dichloromethane. We observe multi-ion receptor-Cl – complexes (2:1, 1:1, 1:2), reinforcing the complexity that emerges when working in low-polarity media. Here, we reveal the dependence of affinity on anion charge density and size and that bulky BArF – counteranions compete for chloride binding. These studies reveal the noninnocence of BArF – anions and strategies to quantify multi-ion species.

Ion pairing

Chiral kinematic theory and converse vortical effects

Response theories in condensed matter typically describe the response of an electron fluid to external electromagnetic fields, while perturbations on neutral particles are often designed to mimic such fields. Here, we study the response of fermions to a space-time-dependent velocity field, thereby sidestepping the issue of gauge charge. First, we use a semiclassical chiral kinematic theory to obtain the local density of current and extract the orbital magnetization. The theory immediately predicts a "converse vortical effect," defined as an orbital magnetization driven by linear velocity. It receives contributions from magnetic moments on the Fermi surface and the Berry curvature of the occupied bands. Then, transcending semiclassics via a complementary Kubo formalism reveals that the uniform limit of a clean system receives only the Berry curvature contribution while other limits sense the Fermi surface magnetic moments too. We propose CoSi as a candidate material and suggest magnetometry of a sample under a thermal gradient to detect the effect. Overall, our study sheds light on the effects of a space-time-dependent velocity field on electron fluids and paves the way for exploring quantum materials using new probes and perturbations.

Chen, Kai [University of Houston]

Developing affordable and efficient heating devices for enhanced live cell imaging in confocal microscopy

Temperature control is crucial for live cell imaging, particularly in studies involving plant responses to high ambient temperatures and thermal stress. This study presents the design, development, and testing of two cost-effective heating devices tailored for confocal microscopy applications: an aluminum heat plate and a wireless mini-heater. The aluminum heat plate, engineered to integrate seamlessly with the standard 160 mm × 110 mm microscope stage, supports temperatures up to 36°C, suitable for studies in the range of non-stressful warm temperatures (e.g., 25-27°C forArabidopsis thaliana) and moderate heat stress (e.g., 30-36°C forA. thaliana). We also developed a wireless mini-heater that offers rapid, precise heating directly at the sample slide, with a temperature increase rate over 30 times faster than the heat plate. The wireless heater effectively maintained target temperatures up to 50°C, ideal for investigating severe heat stress and heat shock responses in plants. Both devices performed well in controlled studies, including the real-time analysis of heat shock protein accumulation and stress granule formation inA. thaliana. Our designs are effective and affordable, with total construction costs lower than $300. This accessibility makes them particularly valuable for small laboratories with limited funding. Future improvements could include enhanced heat uniformity, humidity control to mitigate evaporation, and more robust thermal management to minimize focus drift during extended imaging sessions. These modifications would further solidify the utility of our heating devices in live cell imaging, offering researchers reliable, budget-friendly tools for exploring plant thermal biology.

Plant Sciences

Structure–Property Linkage in Alloys Using Graph Neural Network and Explainable Artificial Intelligence

Deep learning tools have recently shown significant potential for accelerating the prediction of microstructure–property linkage in materials. While deep neural networks like convolution neural networks (CNNs) can extract physics information from 3D microstructure images, they often require a large network architecture and substantial training time. In this research, we trained a graph neural network (GNN) using phase field generated microstructures of Ni-Al alloys to predict the evolution of mechanical properties. We found that a single GNN is capable of accurately predicting the strengthening of Ni-Al alloys with microstructures of varying sizes and dimensions, which cannot otherwise be done with a CNN. Additionally, GNN requires significantly less GPU utilization than CNN and offers more interpretable explanation of predictions using saliency analysis as features are manually defined in the graph. We also utilize explainable artificial intelligence tool Bayesian Inference to determine the coefficients in the power law equation that governs coarsening of precipitates. Overall, our work demonstrates the ability of the GNN to accurately and efficiently extract relevant information from material microstructures without having restrictions on microstructure size or dimension and offers an interpretable explanation.

Chemistry

Self-aligned heterogeneous quantum photonic integration

Integrated quantum photonics holds significant promise for scalable photonic quantum information processing, quantum repeaters, and quantum networks, but its development is hindered by the mismatch between materials hosting high-quality quantum emitters and those compatible with mature photonic technologies. Heterogeneous integration offers a potential solution to this challenge, yet practical implementations have been limited by inevitable insertion losses at material interfaces. Here, we present a self-aligned heterogeneous quantum photonic integration approach that enables near-unity coupling efficiency at the interface. To showcase our approach, we demonstrate Purcell enhancement of a silicon vacancy (SiV) center in diamond induced by a heterogeneous photonic crystal cavity defined by titanium dioxide (TiO 2 ), as well as optical spin control and readout via a TiO 2 photonic circuit. We further show that, when combined with inverse photonic design, our approach enables efficient and broadband collection of single photons from a color center into a heterogeneous waveguide. Our approach is not restricted to SiV centers or TiO 2 ; it has the potential to be broadly applied to integrate diverse solid-state quantum emitters with thin-film photonic devices where conformal deposition is possible. Together, these results establish a practical route to scalable quantum photonic integrated circuits that combine high-quality quantum emitters with technologically mature photonic platforms.

36 MATERIALS SCIENCE

Self‐Propelling Macroscale Sheets Powered by Enzyme Pumps

Nanoscale enzymes anchored to surfaces act as chemical pumps by converting chemical energy released from enzymatic reactions into spontaneous fluid flow that propels entrained nano‐ and microparticles. Enzymatic pumps are biocompatible, highly selective, and display unique substrate specificity. Utilizing these pumps to trigger self‐propelled motion on the macroscale has, however, constituted a significant challenge and thus prevented their adaptation in macroscopic fluidic devices and soft robotics. Using experiments and simulations, we herein show that enzymatic pumps can drive centimeter‐scale polymer sheets along directed linear paths and rotational trajectories. In these studies, the sheets are confined to the air/water interface. With the addition of appropriate substrate, the asymmetric enzymatic coating on the sheets induces chemically driven, buoyancy flows that controllably propel the sheet's motion on the air/water interface. The directionality and speed of the motion can be tailored by changing the pattern of the enzymatic coating, type of enzyme, and nature and concentration of the substrate. This work highlights the utility of biocompatible enzymes for generating motion in macroscale fluidic devices and robotics and indicates their potential utility for in vivo applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH

Light-triggered electrochemical biosensor using singlet oxygen for self-powered operation and glucose detection

This study introduces a light-activated sensing strategy that integrates photosensitization with electrochemical detection. The sensor employs Eosin Y, a photosensitizer that generates singlet oxygen ( 1 O 2 ) via type II photosensitization. Immobilized within a thin polymer matrix on a carbon working electrode, Eosin Y produces 1 O 2 , under green light (520 nm) illumination, initiating a redox process that yields a measurable current. To incorporate biosensing capabilities and enable self-powered operation, this 1 O 2 – mediated process was coupled with glucose oxidase (GOx) to construct a fully operational glucose biosensor. The addition of glucose reverses the current flow by causing GOx to compete for electrons, with the resulting current magnitude correlating with glucose concentration providing a sensitive measure of glucose. The biosensor, as proof-of-principle, demonstrated excellent performance over a range of glucose concentrations (0–73 mM), achieving a detection limit (LOD) of 2.8 mM for steady state photocurrent under oxygen-saturated conditions. This platform leverages light and 1 O 2 as stimuli for tunable, on-demand signal control, offering a novel approach for adaptive, real-time biosensing technologies.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH

Influence of Powder Characteristics and Processing Methods on Creep Performance of Powder Metallurgy Hot Isostatic Pressed SS316

The U.S. nuclear energy expansion goals are driving the demand for manufacturing routes that can rapidly produce large, complex, near net shape components. Powder metallurgy hot isostatic pressing (PM HIP) is an advanced manufacturing technique that can be economically scaled-up, while alleviating the supply chain challenges that forging and casting face in terms of cost and lead time constraints. This makes PM-HIP a viable technology to aid and accelerate large-scale part manufacturing for nuclear applications. However, large-scale qualification and deployment of this technology require a thorough understanding of the influence of powder feedstock quality, powder handling history, hot isostatic pressing (HIP) parameters, and subsequent heat treatment on microstructural evolution and elevated temperature mechanical performance. The present work focusses on 316 austenitic stainless steel (SS316) which is most commonly used in high temperature environments for nuclear applications Results from this study show that PM HIPed SS316 meets ASME tensile requirements at room temperature and at elevated temperature. However, creep performance of PM-HIPed SS316 remains inferior to its wrought counterpart, demonstrating that tensile performance alone is not a reliable metric for long duration high temperature integrity. Further, this report delineates powder derived microstructural features that govern creep damage, with key evidences pointing to “microstructural inheritance” from gas atomized powder feedstocks. Commercial SS316 powders of varying chemical compositions and recycling histories were studies, and the results showed large differences in elemental segregation, oxide surface layers and secondary phase distributions. Multi-scale characterization revealed segregation of chromium, molybdenum, manganese and silicon at the boundaries and the precipitation of manganese-, silicon-, and molybdenum-oxides. During HIP consolidation, these surface oxides transform into decorated prior particle boundaries (PPBs) and grain boundary inclusions that persist through conventional post-HIP solution annealing treatment. The retained oxides in post-HIP microstructures were found to influence grain growth, precipitation behavior, and ultimately creep cavitation and fracture. Such post-HIP heat treatments are therefore limited by a complex trade-off between grain growth, and oxide coarsening which aggravate creep damage by acting as nucleation sites for cavities. The objective of this work is to establish an integrated processing–structure–property framework for PM-HIP 316 stainless steel by investigating the influence of powder feedstock characteristics in pre- and post-HIP processing as well as to understand the significance of post-HIP heat treatment on microstructural evolution and creep properties. The results from this report emphasize the significance of powder feedstock integrity in improving creep performance of PM-HIPed SS316, by highlight the effect of rapid solidification, elemental segregation, oxide formation and powder recycling on microstructural defect inheritance following HIP consolidation. Rather than considering HIP processing, solution annealing, and mechanical performance independently, this report treats powder production, HIP consolidation, post-HIP thermal processing, and creep deformation as interconnected stages within a continuous metallurgical process. The resulting framework will provide a scientific basis for developing feedstock engineering strategies capable of improving long-term reliability of PM-HIP stainless steels and accelerating their qualification for advanced nuclear applications.

Ajjarapu, Pavan [Oak Ridge National Laboratory (OR

Solid-State Syntheses, Crystallographic Spatial Disorders, Thermal Behaviors, and Bandgaps of Hybrid Organic-Inorganic Manganese Halides: A2Mn(Cl/Br)4 (A = NH4+, C(NH2)3+, & C3H4N2+)

By systematically optimizing solid-state synthesis via the concerted use of differential scanning calorimetry and in-situ variable-temperature X-ray diffraction, we report the discovery of four new hybrid organic-inorganic manganese halides A2Mn(Cl/Br)4 (A = NH4+, C(NH2)3+, C3H4N2+), with emphasis on how the organic fragment geometry, polarity, and electron-donating properties influence crystallographic spatial disorders, thermal behaviors, and optical band gaps. With a nonpolar tetrahedral cation, as in (NH4)2MnCl4 (P21/c, mP30) or (NH4)2MnBr4 (C2/c, mC180), the direct optical bandgaps (4.36–4.28 eV) are wider than those with an organic nonpolar planar geometry, as in (C(NH2)3)2MnBr4 (P21/c, mP300, 4.07 eV), or an organic polar planar geometry, as in (C3H4N2+)2MnBr4 (I41/a, tI384, 4.05 eV). Furthermore, the organic components affect the spatial arrangement and dimensionality of the resulting inorganic frameworks comprised of Mn(Cl/Br)6 octahedra, with varying distortions, or spatially disordered MnBr4 tetrahedra. These resulting trends, coupled with the systematic investigation into synthesis, and the motivation behind elucidating the nuanced role of the organic cation, altogether expand upon the phase-space of hybrid materials beyond perovskites and demonstrate the potential for a rational design of hybrid materials with tailored optoelectronic functionalities for advanced energy applications.

Lee, Shannon J.

Breaking the Energy Barrier of Heavy Metal Ion Diffusion in Micropores with Mesoporous 3D Graphene for Fast and Efficient Cu2+ Removal

Efficient removal of heavy metals from water critically depends not only on adsorption capacity but also on ion diffusion kinetics and the associated energy barriers. In conventional carbon adsorbents, severe diffusion confinement within micropores restricts ion transport, resulting in sluggish adsorption kinetics and large apparent activation energies despite high specific surface areas. Here, we demonstrate that this fundamental limitation is overcome by engineering meso/macroporous architectures in the 3D graphene materials synthesized via our discovered alkali-metal reactions with\\\\r\\\\n2\\\\r\\\\nCO. The unique 3D graphene materials possess defect-rich graphene frameworks with interconnected meso/macroporous networks, exhibiting simultaneously high surface area and greatly enhanced meso/macropore volume that enable efficient access to adsorption sites. As a result, the Cu2+ adsorption on 3D graphene proceeds with very low activation energies (4.98 kJ mol–1), which is almost 4 times smaller than on activated carbon (23.1 kJ mol–1). This finding offers a promising platform for efficient and sustainable water purification.

25 ENERGY STORAGE

Long-range magnetic order and relaxor ferroelectricity in a hexagonal high-entropy ferrite

Multiferroics that combine ferroelectricity and magnetic order are attractive for electronic and spintronic technologies, yet chemical disorder that promotes relaxor ferroelectricity usually suppresses long-range magnetic order. Here, we report entropy-stabilized relaxor multiferroicity in epitaxial hexagonal (Tb0.2Dy0.2Ho0.2Lu0.2Yb0.2)FeO3 thin films. Structural, magnetic, dielectric, and synchrotron spectroscopic measurements show the coexistence of relaxor ferroelectricity and long-range ferromagnetic order. We find that improper ferroelectricity remains robust against A-site configurational disorder, while the Fe sublattice preserves magnetic exchange. This separation of the microscopic origins of the polar and magnetic responses enables chemically disordered multiferroicity. Our results establish entropy engineering in hexagonal ferrites as a route toward multifunctional oxide thin films and provide a general design strategy for high-entropy multiferroics.

Miertschin, Duncan [Baylor University]

The effect of gamma ray irradiation on few layered MoSe2: A material for nuclear and space applications

In recent years, emerging two-dimensional (2D) materials, such as molybdenum diselenide (MoSe2), have been at the center of attention for many researchers. This is due to their unique and fascinating physicochemical properties that make them attractive in space and defense applications that include shielding harsh irradiation environments. In this study, we examined the effects of gamma (γ) rays at various doses on the structural, chemical, and optical properties of MoSe2 layers. After the samples were exposed to intense gamma radiation (from a 60Co source) with various exposure times to vary the total accumulated dosage (up to 100 kGy), Raman and photoluminescence spectroscopies were used to study and probe radiation-induced changes to the samples. When compared to pristine materials, very few changes in optical properties were typically observed, indicating good robustness with little sensitivity, even at relatively high doses of gamma radiation. The imaging using scanning electron microscopy revealed a number of nano-hillocks that were connected to substrate alterations. X-ray photoelectron spectroscopies revealed that Mo’s binding energies remained the same, but Se’s binding energies blueshifted. We associated this shift with the decrease in Se vacancies that occurred after irradiation as a result of Mo atoms creating adatoms next to Se atoms. When compared to pristine materials, very few changes in optical, chemical, and structural properties were typically observed. These findings highlight the inherent resilience of MoSe2 in hostile radioactive conditions, which spurs additional research into their optical, electrical, and structural characteristics as well as exploration for potential space, energy, and defense applications.

Materials Science

Computational simulation of asymmetric phase transformation in cracked Li₇La₃Zr₂O₁₂: Variant selection and chemo-mechanical implications

Coupling between microcracks and phase transformation in ion-conducting ceramics can jointly affect mechanical responses and ion transport. In this work we investigate the cubic-to-tetragonal phase transformation in Li₇La₃Zr₂O₁₂ in the presence of a microcrack under hydrostatic loading and quantify its implications for crack-tip stress concentration and Li-ion transport using phase-field and molecular dynamics simulations. The phase transformation exhibits a strong asymmetry between hydrostatic tension and compression. Under tension, the crack edge nucleates one tetragonal variant that amplifies the crack-tip stress intensity and promotes crack opening. Under compression, the crack tip nucleates a different tetragonal variant that enhances the stress-induced crack-closure tendency. Effective Li diffusivity analysis shows faster transport degradation under compression due to accelerated transformation kinetics, exposing a trade-off between mechanical stability and ionic conductivity. These results highlight the intertwined nature of cracking, phase transformation, and ionic transport in ion-conducting oxides and provide mechanistic insights into chemo-mechanical degradation of solid electrolytes.

36 MATERIALS SCIENCE

Decorated Honeycomb Lattice and Successive Magnetic Transitions of the Delafossite Derivative K 4 Ni 5 Te 3 O 16

Here, we report the synthesis and characterization of the delafossite derivative K 4 Ni 5 Te 3 O 16 , which hosts a decorated honeycomb Ni 2+ lattice. Single-crystal X-ray diffraction, electron microscopy, and neutron diffraction establish a noncentrosymmetric Pmm2 crystal structure that combines regular honeycomb units with elongated motifs formed by Ni 2+ trimers along extended edges. Magnetic susceptibility reveals strong antiferromagnetic interactions, while heat capacity measurements identify two successive magnetic transitions at 30 and 12 K. Neutron diffraction shows that these transitions correspond to a progression from partial to full long-range magnetic order on distinct Ni sites, reflecting competition among the various exchange interactions. The resulting magnetic point group, mm2.1′, inherits the lattice polarity and permits high-order magnetoelectric coupling. Consistent with this symmetry, a quadratic magnetic-field-induced polarization is experimentally observed below the magnetic ordering temperature, likely arising from exchange-driven magnetostriction coupled to the polar lattice. These results establish K 4 Ni 5 Te 3 O 16 as an interesting platform for engineering B-site ordering in delafossite derivatives to realize complex quantum magnetism and functional responses.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND